Article citationsMore>>

McCallum, W. and Poonen, B. (2012) The Method of Chabauty and Coleman, Explicit Methods in Number Theory. In: Panoramas et Synthèses, Société Mathématique de France, Paris, 36, 99-117.

has been cited by the following article:

• TITLE: Rational Points on Genus 3 Real Hyperelliptic Curves

  AUTHORS: Brice M. Miayoka, Regis F. Babindamana, Basile G. R. Bossoto

  KEYWORDS: Hyperelliptic Curve, Jacobian, Coleman Integration, Rational Point

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.11 No.4, October 19, 2021

  ABSTRACT: We compute rational points on real hyperelliptic curves of genus 3 defined on whose Jacobian have Mordell-Weil rank r=0. We present an implementation in sagemath of an algorithm which describes the birational transformation of real hyperelliptic curves into imaginary hyperelliptic curves and the Chabauty-Coleman method to find C (). We run the algorithms in Sage on 47 real hyperelliptic curves of genus 3.